Block and multilevel preconditioning for stochastic Galerkin problems with lognormally distributed parameters and tensor product polynomials

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F17%3A00313941" target="_blank" >RIV/68407700:21110/17:00313941 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/17:10371171

Výsledek na webu

<a href="http://www.dl.begellhouse.com/journals/52034eb04b657aea,468587191a97aaba,3cd7c9483550940c.html" target="_blank" >http://www.dl.begellhouse.com/journals/52034eb04b657aea,468587191a97aaba,3cd7c9483550940c.html</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1615/Int.J.UncertaintyQuantification.2017020377" target="_blank" >10.1615/Int.J.UncertaintyQuantification.2017020377</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Block and multilevel preconditioning for stochastic Galerkin problems with lognormally distributed parameters and tensor product polynomials

Popis výsledku v původním jazyce

The stochastic Galerkin method is a popular numerical method for solution of differential equations with randomly distributed data. We focus on isotropic elliptic problems with lognormally distributed coefficients. We study the block-diagonal preconditioning and the algebraic multilevel preconditioning based on the block splitting according to some hierarchy of approximation spaces for the stochastic part of the solution. We introduce upper bounds for the resulting condition numbers, and we derive a tool for obtaining sharp guaranteed upper bounds for the strengthened Cauchy-Bunyakowsky-Schwarz constant, which can serve as an indicator of the efficiency of some of these preconditioning methods. The presented multilevel approach yields a tool for efficient guaranteed two-sided a~posteriori estimates of algebraic errors and for adaptive algorithms as well.

Název v anglickém jazyce

Block and multilevel preconditioning for stochastic Galerkin problems with lognormally distributed parameters and tensor product polynomials

Popis výsledku anglicky

The stochastic Galerkin method is a popular numerical method for solution of differential equations with randomly distributed data. We focus on isotropic elliptic problems with lognormally distributed coefficients. We study the block-diagonal preconditioning and the algebraic multilevel preconditioning based on the block splitting according to some hierarchy of approximation spaces for the stochastic part of the solution. We introduce upper bounds for the resulting condition numbers, and we derive a tool for obtaining sharp guaranteed upper bounds for the strengthened Cauchy-Bunyakowsky-Schwarz constant, which can serve as an indicator of the efficiency of some of these preconditioning methods. The presented multilevel approach yields a tool for efficient guaranteed two-sided a~posteriori estimates of algebraic errors and for adaptive algorithms as well.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal for Uncertainty Quantification

ISSN

2152-5080

e-ISSN

2152-5099

Svazek periodika

7

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

22

Strana od-do

441-462

Kód UT WoS článku

000415634100004

EID výsledku v databázi Scopus

2-s2.0-85035085928